Pith Number

pith:SZSNFO6K

pith:2025:SZSNFO6KAGT2AX6IFVYZIE7RO3

not attested not anchored not stored refs pending

Ultracategories via Kan extensions of relative monads

Joshua Wrigley, Umberto Tarantino

arxiv:2506.09788 v1 · 2025-06-11 · math.CT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SZSNFO6KAGT2AX6IFVYZIE7RO3}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T11:19:56.944903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9664d2bbca01a7a05fc82d719413f176dd4d499f434be5f43d2b07c423eff835

Aliases

arxiv: 2506.09788 · arxiv_version: 2506.09788v1 · doi: 10.48550/arxiv.2506.09788 · pith_short_12: SZSNFO6KAGT2 · pith_short_16: SZSNFO6KAGT2AX6I · pith_short_8: SZSNFO6K

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SZSNFO6KAGT2AX6IFVYZIE7RO3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9664d2bbca01a7a05fc82d719413f176dd4d499f434be5f43d2b07c423eff835

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12de0ce3708c65e72000b661a861518d2d68d0284e185f93faa84c5a03d6e406",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-06-11T14:31:45Z",
    "title_canon_sha256": "bffc815d3dadb8de9abea4d3f855b34a7b777e0a5659b8daffa32f38b50691ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.09788",
    "kind": "arxiv",
    "version": 1
  }
}